Propagation of autoignition basic modelling considerations

Clearly an understanding of the propagation of both the pressure and reaction waves from a hot spot and their possible interactions requires a 

For one dimension, in the x direction, neglecting molecular transport, the equations are. 

This one-step expression for the reaction rate is adequate for a demonstration of some of the general principles involved in the generation of pressure pulses. The equations are used to show the effects of the temperature gradient around a hot spot and the volumetric heat release rate there upon the propagation of autoignition. 

Planar one-dimensional, and cylindrical two dimensional, time-dependent, solutions of equations (7.19) to (7.22) have been presented by Konig et al. [168], for various initial linear temperature gradients away from the hot spot. Their one-dimensional solutions, for po = 4 MPa, EIRTq = 20, and a hot-spot temperature, Tq, of 1000 K, with other property values the 

The thermal explosion mode is entered with a small temperature gradient of 1.25 K/mm. The temporal developments of the fuel coneentration, gas velocity, pressure and temperature fields are shown in Fig. 7.21. The solutions show a uniform increase in pressure to be soon attained, with but low gas velocities, throughout the volume. The apparent speed of propagation of the reaction front away from the centre is higher than the acoustic velocity, a function solely of the initial temperature gradient away from the hot spot. 

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